A Profit Distribution Model of Reverse Logistics Based on Fuzzy DEA Efficiency—Modified Shapley Value

Abstract

Reverse logistics is an important way to realize sustainable production and consumption. With the emergence of professional third-party reverse logistics service providers, the outsourcing model has become the main mode of reverse logistics. Whether the distribution of cooperative profit among multiple participants is fair or not determines the quality of the implementation of the outsourcing mode. The traditional Shapley value model is often used to distribute cooperative profit. Since its distribution basis is the marginal profit contribution of each member enterprise to different alliances, it is necessary to estimate the profit of each alliance. However, it is difficult to ensure the accuracy of this estimation, which makes the distribution lack of objectivity. Once the actual profit share deviates from the expectation of member enterprise, the sustainability of the reverse logistics alliance will be affected. This study considers the marginal efficiency contribution of each member enterprise to the alliance and applies it to replace the marginal profit contribution. As the input and output data of reverse logistics cannot be accurately separated from those of the whole enterprise, they are often uncertain. In this paper, we assume that each member enterprise’s input and output data are fuzzy numbers and construct an efficiency measurement model based on fuzzy DEA. Then, we define the characteristic function of alliance and propose a modified Shapley value model to fairly distribute cooperative profit. Finally, an example comprising of two manufacturing enterprises, one sales enterprise, and one third-party reverse logistics service provider is put forward to verify the model’s feasibility and effectiveness. This paper provides a reference for the profit distribution of the reverse logistics.

Research on Shared Logistics Decision Based on Evolutionary Game and Income Distribution

“…Li et al [29] studied the profit distribution problem of urban joint distribution alliances by incorporating four criteria (enterprise operation, customer satisfaction, environmental sustainability, and information technology) into the improved Shapley value model. Song et al [30] constructed a fuzzy DEA-based efficiency metric model. Based on this, they proposed an improved Shapley value model to equitably allocate cooperative profits.…”

Input/Output Variables Selection in Data Envelopment Analysis: A Shannon Entropy Approach

“…Notably, the main limitation of the study is that the proposed DEASE approach is not capable to be used under data uncertainty. Accordingly, for future research, the DEASE approach can be proposed under uncertain data, including fuzzy [76][77][78][79][80][81][82][83][84][85][86][87][88][89][90], stochastic [91][92][93][94][95][96][97][98][99][100][101][102], and interval [103][104][105][106][107][108][109][110][111][112][113] data. Additionally, the DEASE approach can be combined with machine learning approaches for the prediction of input and output data, and consequently, evaluation of the future performance of DMUs [114][115][116][117][118][119][120][121][122]…”

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“…As a common method in cooperative games, the Shapley value is widely used in the studying profit distribution. In studying reverse logistics benefit distribution, Song [17] constructed a fuzzy DEAbased efficiency measurement model and proposed an improved Shapley value model for fair distribution of cooperative profits. Based on the traditional Shapley algorithm, Zhou et al [18] proceeded from stakeholders to establish a benefit distribution model for IPD team, which improved the benefit distribution mechanism.…”